welcome back to control system lectures in this video we're going to begin our conversation on PID control this video is just an introduction to the topic and we'll hopefully provide some good background information on PID controllers now to describe what PID control is and why we use it let me first describe more generally what a controller is and one way to write an open loop system is like this where inputs act on a plant or the system to be controlled and then some output signal is generated often in these open loop scenarios the performance of
the system isn't good enough to meet your requirements let me give you an example of what I mean you're tasked to build a robot that needs to move from this spot here over to this red X you could figure out how fast the robot moves and then from that determine how long the robot needs to drive for before it gets to the Red X this type of commanding is called open loop because the amount of time the robot drives is not adjusted based on the actual position of the robot and open loop commanding is perfectly
fine for systems that don't change much or where accuracy isn't as important however what if there's some dirt in one of the wheels and the robot veers off to the side or if the robot slightly faster than you had predicted in both of these cases the robot won't stop on the Red X because it has no way of compensating for these errors and making adjustments on its own now the solution then is feedback control which is essentially means you're sensing the output of the plant and feeding it back so that the system can make adjustments
accordingly now in a feedback system there's a reference signal and this is the desired value or the ultimate goal and you compare that to the measured value and what you're left with is the error or the Delta between where you are and where you want to be so in the case of the robot the error would be the difference from the reference position which is the distance from the start to the red X in meters and the robot current position which is measured by the robot also in meters so at this point we need to
figure out how to convert an error signal that has units the same as the output of the plant into an input signal that has units that may or may not be the same as the output and in addition to just changing the units the error needs to be adjusted in such a way that the input into the robot causes it to eventually reach the Red X and this is exactly what a controller does it takes the error signal and converts it into a command that is then sent into the plant and one of the goals
of a control engineer is to design this controller so that as time progresses the error or the difference between the current location and the goal is driven to zero and zero error means that the measured position is exactly where you want it to be which means that the system meets all of its requirements well at least this particular one now there's many types of controllers and we're going to touch on a lot of them as these videos progress however in this lecture I'm only going to talk about PID controllers and its variations I'll explain what
I mean by that in a second the PID controller is a great place to start because it's simple efficient and effective in a wide array of applications in fact it's the majority of controller types in industrial applications so it's well worth learning let me start with the term PID P ID is an acronym and it stands for proportional integral derivative and each of these terms describe how the error term is treated prior to being summed and sent into the plant in one of its block diagram forms a PID controller can be written like this in
the proportional path the error term is multiplied by a constant KP in the integral path the error is multiplied by Ki and then integrated and in the derivative path it's multiplied by KD and then differentiated the three paths are then summed together to produce the controller output now the three k terms are called gains and they can be adjusted or tuned to a particular plant with a defined set of requirements and by changing these values you're adjusting how sensitive the system is to each of these different paths either the p i or D path let
me explain what I mean with a few plots here let's say the error in the system is changing over time like this red line in the proportional path the output is the error scaled by the gain KP so you can see here that when the error is large the proportional path will produce a large output when the error is zero the output in the path is zero and when it's negative the output is negative in the integral path as the error moves over time the integral will continually sum it up and multiply it by the
constant Ki in this plot it's easy to see that the integral path is the area under the curve where this blue section is positive area and this green section here is negative area now the integral path is used to remove constant errors in a control system since no matter how small the constant error eventually the summation of that error will be significant enough to adjust the controller output now in the derivative path it's the rate of change of the error that contributes to the output signal when the change in error is moving relatively slowly like
it is at the beginning here then the derivative path is small and the faster the error changes the larger the derivative path becomes now at this point you can just sum up each of these three paths and you've got the output of a PID controller but you don't always need all three paths you can remove a path completely by setting its Associated gain to zero when you do this you generally refer to the controller with the letters of the path that are left for example you can have a proportional integral controller or Pi if you
set k k d to zero and just a p controller if KD and Ki are both zero so why would you simplify the controller like that why not just make the biggest best controller you can with all paths intact and super complicated well typically when I'm designing a control law I try to make the logic as simple as I can while still meeting all design requirements I do this for several reasons one is a simple controller is easy to implement two a simple controller is easy to tune test and troubleshoot when there's problem s and
three a simple controller is easy for other people to understand which is important when you work in a large project and interface with other groups that have to buy into the control Logic for example a software Hardware team that has to implement it so simple controllers can save you time and money over the life of the program as long as they still meet your design requirements and this is why despite having a lot of really complicated Control Systems out there the majority of Industry still uses PID control or some variation now you're probably thinking right
now all right you've given me the definition of a PID controller but that really didn't help that much because if you're like me I don't usually understand something by definition alone and I need some examples for it to sync in but I want to end this video here so that it doesn't become too long that you lose interest but next week I'm going to have a video that runs through a thought exercise on PID control and then show some of the math to back up that exercise I'm going to link a video here in this
box once it's complete so you can just click on through if this box is empty that means I haven't finished it yet so if you don't want to miss it and you haven't subscribed already don't forget to hit the Subscribe button and thanks for watching
